It doesn't sound like much at first: a blurred warble, fingers idly roaming the keyboard of an upright piano. Thom Yorke sits with his back slightly hunched and half-turned away from the audience at New York's Roseland Ballroom. He seems to be humming and playing to himself as he waits for the rest of Radiohead – guitarist Ed O'Brien, bassist Colin Greenwood, drummer Phil Selway and Colin's younger brother, guitarist Jonny Greenwood – to finish switching instruments for the next song.

But then a chorus comes out of the haze. "This one goes out to the one I left behind," Yorke sings from R.E.M.'s 1987 hit "The One I Love," hitting the piano with affectionate emphasis before easing into the climbing hook and irregular rhythm of "Everything in Its Right Place" from Radiohead's 2000 album, Kid A. Tonight is the first of the British band's September 28th and 29th shows in New York, part of a belated promo blitz – including appearances on Saturday Night Live and The Colbert Report – for Radiohead's eighth studio album, The King of Limbs.

At Roseland, though, Yorke has R.E.M. – especially their singer Michael Stipe – on his mind. As a teenager, Yorke was "really bitten" by that band, according to Colin. "It was Michael's ability," the bassist told me recently, "to be emotional and moving but oblique at the same time." Yorke later became friends with Stipe after Radiohead opened shows on R.E.M.'s Monster tour in 1995. And a week ago, on September 21st, when R.E.M. announced their breakup after 31 years together, Stipe sent Yorke an advance warning by text.

"Everything was going onto the stage""It was Michael absolutely, the way he dealt with the stage," Yorke says the day before his Roseland tribute in a Manhattan hotel, drinking tea made white with milk and recalling what he learned from Stipe about fighting the spotlight and taking charge of your stardom. "He would mumble this crap between songs, like he was talking backwards. He wasn't even attempting to be like, 'Hey, everybody, how ya doing?' It was this completely evasive thing. But at no point did you ever get the sense he was running away. Everything was just going into that, onto the stage."

Yorke describes the terror he felt at the mike on Radiohead's early tours, acting out the seething distress in "Creep" – their Top 40 breakthrough in 1993 – and "My Iron Lung." "I was freaking out," he says, "like 'What the fuck am I doing here?' It was like I was driving a car or flying a plane with my eyes closed: 'I'll hit something eventually.'

"I understand now what Michael was doing," Yorke says. "The things he was choosing not to do, not to be, were even more powerful than what he did. There was this air of deliberately a little fucked up." Yorke grins in admiration. "I liked that."

Stipe in orbitYorke first saw R.E.M. live on their Green tour, at London's Wembley Arena in June, 1989. "Most of my friends had seen them before that," he notes. "Michael told me later that he had a bad time at that show, throwing things around after. The first time I really saw them properly was when we toured with them" – two dozen Monster shows in Europe and the U.S. in the summer and fall of 1995. "Then I was watching Michael every night.

"He was quite distant during that," Yorke admits. "It was kind of odd. He was in orbit. His place was on the stage. And when he was off stage, he was not there at all. Occasionally, after a few drinks, he would be alright. But generally he was a little bit strange. Obviously now, I totally understand it.

"But what I liked about watching R.E.M. – and this is something our band picked up straight away – was how they allowed shit to happen, not trying to add to it but just fucking stand there,. waiting for the fire to start," Yorke goes on. "Sometimes it would be mid-set, and it's still not kicking off yet. But no one's freaking out. They're staying with it" – Yorke pauses dramatically – "and then bang!"

The end of an era"That was the first time I'd seen that in a big environment," Yorke says. "You see it with little bands in small places. But to do that in a large space and get away with it, without using any tricks, was cool. I've seen the same thing in Neil Young – standing there, stamping his foot, looking down as he plays, just letting that do it. It's very purist. It ain't Lady Gaga." Yorke claims he was not surprised by Stipe's text: "I think it was kind of going one way for awhile. I just wanted to check that Michael was alright." In fact, the two singers spent much of Radiohead's week in New York together.

"It was cool, man – it was good," Yorke confirms. "We hung out. He came to Saturday Night Live. And it was really nice to see him – very clear, very present and okay with it."